Optimal General Factor Problem and Jump System Intersection

  title={Optimal General Factor Problem and Jump System Intersection},
  author={Yusuke Kobayashi},
  booktitle={Conference on Integer Programming and Combinatorial Optimization},
  • Yusuke Kobayashi
  • Published in
    Conference on Integer…
    2 September 2022
  • Mathematics, Computer Science
In the optimal general factor problem, given a graph $G=(V, E)$ and a set $B(v) \subseteq \mathbb Z$ of integers for each $v \in V$, we seek for an edge subset $F$ of maximum cardinality subject to $d_F(v) \in B(v)$ for $v \in V$, where $d_F(v)$ denotes the number of edges in $F$ incident to $v$. A recent crucial work by Dudycz and Paluch shows that this problem can be solved in polynomial time if each $B(v)$ has no gap of length more than one. While their algorithm is very simple, its… 
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